NDT2, Sadler's Wells, London ENB Late at Tate, Duveen Gallery, Tate Britain, London

Dutch courage, Dutch old masters, tulips and coffee shops that don't smell of coffee. By rights, contemporary dance should leap similarly to mind as one of Holland's gifts to the world.

Nederlands Dans Theater sprang to life half a century ago when a chunk of the national ballet company broke free to forge a style of their own. NDT2 was born a generation later, initially as a training squad but increasingly a distinct phenomenon, and phenomenal.

Youth, skilled and drilled to extremity, has a spellbinding aura of its own. These 17- to 23-year-olds feel themselves immortal. Energy is a given, speed a plus. Now too, they're getting infusions of creative oxygen from Swedish prodigy Alexander Ekman, an NDT2 alumnus whose choreographic career has already spilled over into stage design and film. Better still, Ekman knows how to have a laugh, pricking the bubble of adolescent angst that can tip NDT2's repertory into the absurd.

Ekman's 2010 work Cacti is smart and different, its movement generated from a sculptural installation of 16 dazzling white squares. These in turn become plinths on which the 16 dancers pat-a-cake rhythmic responses to a mash-up of Haydn and Beethoven, with added percussion from the slapping of cheeks and sucking of teeth. This crisply unified movement has comedy, too, with its boogying mix of hand-jive, sport and martial arts, and the introduction of 16 succulents in pots, the titular cacti.

A central duet similarly pokes fun at our endless search for meaning, the couple's taped voices commenting laconically as they dance. "Please be careful with my head," says the guy as the girl makes a move to spin him under her hand. "This part feels weird," she mutters as they lurch together in an asymmetrical embrace. For once, a choreographer has passed the ball back to the audience, making them feel 100 per cent better about not knowing "what it means" – a cheering postmodern take on Postmodernism.

I could have done with a voice in my ear during Jiri Kylian's Gods and Dogs, a dimly lit, possibly Jungian, dreamscape through which eight mostly bare-chested dancers wander with vaguely canine intent, coil-sprung moves alternating with pawing and scratching. At one point a blobby object descends from the dark ceiling and changes shape in the gloom – is it a dog? God? A dog-god? The only certainty is the daring of larding a Beethoven string quartet with electronic beats – nothing's sacred at NDT.

Earlier, Passe-Partout, an oblique, no, to be frank, obscure, country-house mystery in the manner of The Woman in Black, showcased the company's technique in sleek choreography by Paul Lightfoot and Sol Leon. Who cares what it means when the shrouded chatelaine is showing pert bare breasts and the guys are straight out of Abercrombie & Fitch? Youth ... catch a whiff of it on the coming tour.

I've often wondered why art galleries (which have the space, and the décor) don't make more of the connection between dance and painting. The climax of English National Ballet's week-long residency at Tate Britain showed unequivocally why they don't.

Temporary stage-blocks clatter. Domed ceilings produce a cavernous echo. And the struggle to admit a few hundred after-work Picasso-lovers into a pillared room while several thousand more clamour to shoulder their way in has the staff's walkie-talkies in meltdown. What a scrum! But for those who did manage to sight more than the odd clavicle bobbing above a sea of heads, the effort was repaid. Best of several new short ballets relating to pictures in the current exhibition was Stina Quagebeur's take on Picasso's The Three Dancers, catching its Jazz Age strangeness, a ménage à trois curtailed by violent death.

More memorable still was the clip from Balanchine's Apollo, if only for the rare thrill of seeing (for the sharp-elbowed few) ENB principals up close, in all their statuesque magnificence.

NDT2: touring till the end of March (www.danceconsortium.com)

Dance choice

Shobana Jeyasingh marks her company's 25th anniversary with a revision of 1988's Configurations, the work in which she first set out her stall, fusing classical Indian bharata natyam with fleet-footed contemporary dance. It's paired with a new work set to music by record producer Niraj Chag. At London's Linbury Studio, Tue to Sat.